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March 31, 2026Open Access

Adjacent-Transfer Theorem Search: A Validated Five-Theorem Cluster for Balanced Independent Sets on Ladder-Derived Graphs

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Authors

BSBrian Philippe M. Saturnino

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Overview

Case study demonstrates theorem search for balanced independent sets in specific graph families, highlighting proof validation.

Key Points

  • This research aims to explore theorem search methods for balanced independent sets in ladder-derived graph families.
  • Analyzed five types of ladder-derived graphs: ladders, prisms, Mobius ladders, and their diagonal counterparts.
  • Followed a structured workflow including conjecture compression and validated proof routes.
  • Generated exact formulas for maximum balanced independent set sizes with fixed parity-class partitions.
  • Developed a validated cluster of five theorems related to independent sets.
  • Presented lower-bound constructions and zero-sum constraints for balancedness.
  • Identified novelty status, with some theorems carrying risks of prior art.

Cite This Study

Brian Philippe M. Saturnino (2026) studied this question.

synapsesocial.com/papers/69cb6526e6a8c024954b944ehttps://doi.org/10.5281/zenodo.19304215
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